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Third attempt

Posted By: Timothy Chow
Date: Saturday, 2 March 2013, at 3:43 a.m.

In Response To: Another backgammon puzzle (Timothy Chow)

What I said in my last post still doesn't make sense. Here's my third and final attempt.

Say that two backgammon games are the same if they eventually agree, i.e., if after some finite number of rolls, the game positions coincide, and everything stays exactly the same after that. (So in particular, any two games that terminate after a finite number of rolls are considered the same.) Are there infinitely many distinct backgammon games in this sense?

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